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Comparison principle of very weak solutions for nonhomogeneous elliptic equations. (English) Zbl 1463.35134

Summary: Under some suitable assumptions, a comparison principle of very weak solutions for quasi-linear elliptic equation \(-{\mathrm{div}}A(x, \nabla u) = f(x, u)\) is given by using McShane extension theorem to construct the Lipschitz continuous test function, and the corresponding results of some homogeneous equations are generalized.

MSC:

35B51 Comparison principles in context of PDEs
35D30 Weak solutions to PDEs
35J62 Quasilinear elliptic equations